Semantic communication has emerged as a promising technology for enhancing communication efficiency. However, most existing research emphasizes single-task reconstruction, neglecting model adaptability and generalization across multi-task systems. In this paper, we propose a novel generative semantic communication system that supports both image reconstruction and segmentation tasks. Our approach builds upon semantic knowledge bases (KBs) at both the transmitter and receiver, with each semantic KB comprising a source KB and a task KB. The source KB at the transmitter leverages a hierarchical Swin-Transformer, a generative AI scheme, to extract multi-level features from the input image. Concurrently, the counterpart source KB at the receiver utilizes hierarchical residual blocks to generate task-specific knowledge. Furthermore, the task KBs adopt a semantic similarity model to map different task requirements into pre-defined task instructions, thereby facilitating the feature selection of the source KBs. Additionally, we develop a unified residual block-based joint source and channel (JSCC) encoder and two task-specific JSCC decoders to achieve the two image tasks. In particular, a generative diffusion model is adopted to construct the JSCC decoder for the image reconstruction task. Experimental results show that our multi-task generative semantic communication system outperforms previous single-task communication systems in terms of peak signal-to-noise ratio and segmentation accuracy.